Nonlinear Volterra integral equations can arise in systems
whenever there is feedback and filtering. Usually these are
analyzed by deriving equivalent differential models and then using
standard dynamical systems methods. However, the presence of noise
in these models usually puts them beyond differential equations,
and one must consider the Volterra integral equations directly.
The purpose of this paper is to apply a random perturbation method
to a canonical network from mathematical neuroscience that has
parametric noise, and to demonstrate how the results can be used
to estimate the loss of information due to cycle slipping, which
corresponds to noise-induced spurious firing in the network.